The present invention relates to a resistor circuit for controlling the resistance to be desirable, and more particularly to a resistor circuit for variably controlling a MOS resistor by controlling the gate voltage of a MOS transistor.
In more detail, the present invention relates to a resistor circuit in which a reference resistor circuit employing a MOS resistor is disposed, which controls the gate voltage of a MOS such that a voltage generated in the reference resistor circuit is controlled to be the same as a reference voltage (that is, a resistance of the reference resistor circuit is controlled to be constant), and controls the gate voltage of a MOS in a variable resistor circuit including a MOS resistor with reference to the gate voltage of the MOS in the reference resistor circuit in order to follow the resistance of the MOS resistor in the reference resistor circuit. In particular, the present invention relates to a resistor circuit for realizing operations for allowing a variable MOS resistor to follow a reference MOS resistor in terms of the resistance even in the case where the drain-source voltage of the variable MOS resistor and that of the reference MOS resistor are not the same.
A large number of transistor elements having functions including switching, oscillating, amplifying, and the like are implemented in a semiconductor integrated circuit (IC). A transistor with a MOS structure which has three layers including a metal layer, a silicon oxide film layer, and a silicon semiconductor layer may be indicated as a representative example of field-effect transistors (FETs). A MOSFET employing an n-type semiconductor substrate is called a PMOS. A MOSFET employing a p-type semiconductor substrate is called an nMOS.
A field-effect transistor has three electrodes including the source, the drain, and the gate. A MOS transistor has current-voltage characteristics in which a channel is generated on a substrate surface between the source region and the drain region, and a drain current Id flows if a gate voltage Vgs is increased to be greater than or equal to a threshold voltage Vth in a state where the source electrode and a substrate electrode are grounded and a constant voltage Vds is applied to the drain electrode. The MOS transistor can be treated as a resistor unit having a MOS resistor R=Vds/Id by utilizing such characteristics.
Here, the drain current Id and the drain-source voltage Vds at a triode region of the MOS are expressed by Eq. (1) given below (for example, see Non-Patent Document 1).
                              I          d                =                  μ          ⁢                                          ⁢                      C            OX                    ⁢                                    W              L                        ⁡                          [                                                                    (                                                                  V                        gs                                            -                                              V                        th                                                              )                                    ⁢                                      V                    ds                                                  -                                                      1                    2                                    ⁢                                      V                    ds                    2                                                              ]                                                          (        1        )            
Here, if the drain-source voltage Vds is sufficiently small and Vds<<2(Vgs−Vth) is assumed, the drain current Id can be approximated by using Expression (2) given below.
                              I          d                ≈                  μ          ⁢                                          ⁢                      C            OX                    ⁢                      W            L                    ⁢                      (                                          V                gs                            -                              V                th                                      )                    ⁢                      V            ds                                              (        2        )            
Therefore, the MOS resistor R=Vds/Id at the triode region is expressed by Eq. (3) given below with the use of the approximate expression. The MOS resistor R in this case does not depend on the drain-source voltage Vds, and the resistance can be controlled by the gate voltage Vgs.
                    R        =                                            V              ds                                      I              d                                =                      1                          μ              ⁢                                                          ⁢                              C                OX                            ⁢                              W                L                            ⁢                              (                                                      V                    gs                                    -                                      V                    th                                                  )                                                                        (        3        )            
In contrast, if the condition Vds<<2(Vgs−Vth) is not satisfied, the MOS resistor R depends on the drain-source voltage Vds, and thereby the MOS resistor R is expressed by Eq. (4) given below. In this case, only the gate voltage Vgs can no longer control the MOS resistor.
                    R        =                                            V              ds                                      I              d                                =                      1                          μ              ⁢                                                          ⁢                              C                OX                            ⁢                              W                L                            ⁢                              (                                                      V                    gs                                    -                                      V                    th                                    -                                                            1                      2                                        ⁢                                          V                      ds                                                                      )                                                                        (        4        )            
Here, it is necessary that the drain-source voltage Vds decrease or the gate voltage Vgs increase in order to satisfy the approximate condition Vds<<2(Vgs−Vth) for MOS resistors. It is necessary that the resistance decrease or a current of the resistor circuit decrease in order to decrease the drain-source voltage Vds; however, disadvantages occur in terms of resistance-precision. Moreover, if the gate voltage Vgs is maintained large, it is difficult to realize a variable resistance which can be varied over a wide range since the gate voltage Vgs cannot be changed by a large amount. Therefore, the use of MOS resistors according to the approximate expression given by Eq. (3) has technical problems.
In addition, MOS resistors have other technical problems of element-to-element variation and sensitiveness to temperature. Thus, the following design method is widely employed. The method includes disposing a reference resistor circuit which employs a MOS resistor, controlling the gate voltage of a MOS such that a voltage generated in the reference resistor circuit is controlled to be the same as a reference voltage, that is, the resistance of the reference resistor circuit is controlled to be constant, and controlling the gate voltage of a MOS in a variable resistor circuit including a MOS resistor with reference to the gate voltage of the MOS in the reference resistor circuit.
For example, a variable resistor circuit described in Patent Document 1 is configured such that each of the MOS resistors is controlled to have the same resistance by providing the gate voltage of a transistor M1 serving as a variable MOS resistor to a transistor M2 serving as a reference MOS resistor. In the variable resistor circuit, the drain-source voltage generated in the transistor 2 serving as the reference MOS resistor is input to a positive terminal of an OP amplifier 7, and the voltage applied to a resistor Re is input to a negative terminal thereof. The gate voltage of the transistor M2 is controlled such that no potential difference between these voltages exists, and thereby the resistance of the reference MOS resistor is controlled to be the same as Re (for example, see FIG. 1 of Patent Document 1).
In the variable resistor circuit including such a reference MOS resistor and a variable MOS resistor, it is necessary to detect the potential Vds between the drain and source of the reference MOS resistor by causing a drain-source current Id to flow since it is necessary to control the resistance of the reference MOS resistor.
However, if Vds becomes large due to supply of the drain-source current Id, the approximate expression such as Expression (2) no longer holds. Therefore, Eq. (3) cannot be satisfied. In this case, MOS resistors become affected by the drain-source voltage Vds; however, the same drain-source voltage is not generated at the reference MOS resistor and the variable MOS resistor on every occasion. Thus, the variable MOS resistor is not guaranteed to have the same resistance as that of the reference MOS resistor even if the same gate voltage as that of the reference MOS resistor is applied to the variable MOS resistor. That is, desired operational characteristics cannot be obtained for the variable resistor circuit.
In addition, it is necessary that the drain-source voltage Vds of both of the MOS resistors be the same in order to improve resistance-following capability for the variable MOS resistor against the reference MOS resistor. In this case, it is necessary to cause a current to flow through the variable MOS resistor; however, there are disadvantages in terms of distortion, power consumption, and an output voltage in a low-voltage operation. Moreover, in the case where, for example, the resistor is employed as a load of a differential amplifier, it is often desired that no potential for the drain-source voltage Vds exist in the variable MOS resistor.
[Patent document 1]
Japanese Unexamined Patent Application Publication No. 2003-204247, FIG. 1.
[Non-Patent Document 1]
Behzad Razavi, “Analog CMOS Shuseki-kairo no Sekkei Kiso-hen”.